1. **State the problem:** We have 5000 tickets sold at 1 each for a raffle. Prizes are: - 1 prize of 700 - 3 prizes of 300 - 5 prizes of 10 - 20 prizes of 5 We want to find the expected value $E(X)$ of the amount won if you buy 1 ticket. 2. **Formula for expected value:** $$E(X) = \sum (\text{value of prize} \times \text{probability of winning that prize})$$ 3. **Calculate probabilities:** - Probability of winning 700: $\frac{1}{5000}$ - Probability of winning 300: $\frac{3}{5000}$ - Probability of winning 10: $\frac{5}{5000}$ - Probability of winning 5: $\frac{20}{5000}$ - Probability of winning nothing: $1 - \frac{1+3+5+20}{5000} = 1 - \frac{29}{5000} = \frac{4971}{5000}$ 4. **Calculate expected value:** $$E(X) = 700 \times \frac{1}{5000} + 300 \times \frac{3}{5000} + 10 \times \frac{5}{5000} + 5 \times \frac{20}{5000} + 0 \times \frac{4971}{5000}$$ 5. **Simplify each term:** $$= \frac{700}{5000} + \frac{900}{5000} + \frac{50}{5000} + \frac{100}{5000} + 0$$ 6. **Sum the numerators:** $$= \frac{700 + 900 + 50 + 100}{5000} = \frac{1750}{5000}$$ 7. **Simplify the fraction:** $$= \frac{\cancel{1750}^{350}}{\cancel{5000}^{1000}} = \frac{350}{1000} = 0.35$$ **Final answer:** $$E(X) = 0.35$$ So the expected value of the raffle ticket is 0.35 dollars, meaning on average you expect to win 35 cents per ticket bought.